Q1: [25] Non-official Mother Tongue in Canada in 2021 The number of Canadians whose mother tongue is other than English or French hits a record high in 2021 census. English and French remain the dominant languages according to Statistics Canada, but the number of people who speak a non-dominant language at home grew to 4.6 million, or roughly 13 per cent of the population. The following table shows the percentage of population by provinces and territories whose mother tongue is other than English or French. Provinces/Territories Non-official mother tongue (%) Quebec 13.9 Newfoundland and Labrador 2.5 Prince Edward Island 8.5 Nova Scotia 6.5 New Brunswick 4.3 Ontario 26.9 Manitoba 22.4 Saskatchewan 14.2 Alberta 21.5 British Columbia 27.9 Yukon 11.8 Northwest Territories 17.1 Nunavut 54.9 Assuming the percentage of non-official mother tongue speakers at University of Ottawa in 2022 summer was reflective of the provincial rate (i.e., Ontario), a Telfer student took a random sample of 200 University of Ottawa students, where 56 were non-official mother tongue speakers. Do you think the proportion of the University of Ottawa students who spoke non-official mother tongue in 2022 summer was different than that of Ontario population reported by Statistics Canada? (a) [10] Test at 5% level of significance whether the proportion of University of Ottawa students speaking non-official mother tongue is different than that of Ontario popula- tion reported by Statistics Canada. Use both critical value and p-value approach showing detailed manual calculation of the steps of hypotheses (hypotheses, decision zone, critical value, p-value, decision with justification). (Manual Calculation) (b) [7] For testing the same hypotheses, calculate manually an appropriate 95% confidence interval for the population proportion of University of Ottawa students speaking the non-official mother tongue in 2022 summer. Interpret the confidence interval. Does this interval allow you to make the same conclusion as in part (a)? Explain. (Manual Calculation) (c) [3] How large sample size would you need to estimate, within 4%, the true proportion with 90% confidence? Assume there is no prior knowledge of p. (Manual Calcula- tion)Second decimal place in a 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0000 -3.9 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.7 0.0001 0.0001 0.0001 0.0001 D.0001 0.0001 0.0001 0.0001 0.0002 0.0002 -3.6 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0,0002 0.0002 0.0002 0.0002 -3.5 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 -3.4 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005 -3.3 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007 -3.2 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0010 -3.1 0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0013 -3.0 0.0014 0.0014 0.0015 0.0015 0.0016 0.0016 0.0017 0.0018 0.0018 0.0019 -2.9 0.0019 0.0020 0.0021 0.0021 0.0022 0.0023 0.0023 0.0024 0.0025 0.0026 -2.8 0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035 -2.7 0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0045 0.0047 -2.6 0.0048 0.0049 0.0051 0.0052 0.0054 0.0055 0.0057 0.0059 0.0060 0.0062 -25 0.0064 0.0066 0.0068 0.0069 0.0071 00073 0.0075 0.0078 0.0080 0.0082 -2.4 0.0084 0.0087 0.0089 0.0091 0.0094 0.0096 0.0099 0.0102 0.0104 0.0107 -2.3 0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0129 0.0132 0.0136 0.0139 -2.2 0.0143 0.0146 0.0150 0.0154 0.0158 0.0162 0.0166 0.0170 0.0174 0.0179 -2.1 0.0183 0.0188 0.0192 0.0197 0.0202 0.0207 0.0212 0.0217 0.0222 0.0228 -2.0 0.0233 0.0239 0.0244 0.0250 0.0256 0.0262 0.0268 0.0274 0.0281 0.0287 -1.9 0.0294 0.0301 0.0307 0.0314 0.0322 0.0329 0.0336 0.0344 0.0351 0.0359 -1.8 0.0367 0.0375 0.0384 0.0392 0.0401 0.0409 0.0418 0.0427 0.0436 0.0446 -1.7 0.0455 0.0465 0.0475 0.0485 0.0495 0.0505 0.0516 0.0526 0.0537 0.0548 -J.6 0.0559 0.0571 0.0582 0.0594 0.0606 0.0618 0.0630 0.0643 0.0655 0.0668 -1.5 0.0681 0.0694 0.0708 0.0721 0.07.35 0.0749 0.0764 0.0778 0.0793 0.0808 -1.+ 0.0823 0.0838 0.0853 0.0869 0.0885 0.0901 0.0918 0.0934 0.0951 0.0968 -1.3 0.0985 0.1003 0.1020 0.1038 0.1056 0.1075 0.1093 0.1112 0.1131 0,1151 -1.2 0.1170 0.1190 0.1210 0.1230 0.1251 0.1271 0.1292 0.1314 0.1335 0.1357 -1.1 0.1379 0.1401 0.1423 0.1446 0.1469 0.1492 0.1515 0.1539 0.1562 0.1587 -1.0 0.1611 0.1635 0.1660 0.1685 0.1711 0.1736 0.1762 0.1788 0.1814 0.1841 09 0.1867 0.1894 0.1922 0.1949 0.1977 0.2005 0.2033 0.2061 0.2090 0.2119 0. 8 0.2148 0.2177 0.2206 0.2236 0.2266 0.2296 0.2327 0.2358 0.2389 0.2420 -0.7 0.2451 0.2483 0.2514 0.2546 0.2578 0.2611 0.2643 0.2676 0.2709 0.2743 -0.6 0.2776 0.2810 0.2843 0.2877 0.2912 0.2946 0.2981 0.3015 0.3050 0.3085 0.3121 0.3156 0.3192 0.3228 0.3264 0.3300 0.3336 0.3372 0.3409 0.3446 03483 0.3520 0.3557 0.3594 0.3632 0.3669 0.3707 0.3745 0.3783 0.3821 -0.3 0.3859 0.3897 0.3936 0.3974 0.4013 0.4052 0.4090 0.4129 0.4168 0.4207 -0.2 0.4247 0.4286 0.4325 0.4364 0.4404 0.4443 0.4483 0.4522 0.4562 0.4602 -0.1 0.4641 0.4681 0.4721 0.4761 0,4801 0.4840 0.48:80 0.4920 0.4960 0.5000 -0.0 For z S -3.90, the areas are 0.0000 to four decimal places.